Investigating Confidence Intervals of Item Parameters When Some Item Parameters Take Priors in the 2PL and 3PL Models.

To reduce the chance of Heywood cases or nonconvergence in estimating the 2PL or the 3PL model in the marginal maximum likelihood with the expectation-maximization (MML-EM) estimation method, priors for the item slope parameter in the 2PL model or for the pseudo-guessing parameter in the 3PL model can be used and the marginal maximum a posteriori (MMAP) and posterior standard error (PSE) are estimated. Confidence intervals (CIs) for these parameters and other parameters which did not take any priors were investigated with popular prior distributions, different error covariance estimation methods, test lengths, and sample sizes. A seemingly paradoxical result was that, when priors were taken, the conditions of the error covariance estimation methods known to be better in the literature (Louis or Oakes method in this study) did not yield the best results for the CI performance, while the conditions of the cross-product method for the error covariance estimation which has the tendency of upward bias in estimating the standard errors exhibited better CI performance. Other important findings for the CI performance are also discussed.

Development of an Individualized Responsive Feeding Intervention-Learning Early Infant Feeding Cues: Protocol for a Nonrandomized Study.

BACKGROUND: Responsive infant feeding occurs when a parent recognizes the infant's cues of hunger or satiety and responds promptly to these cues. It is known to promote healthy dietary patterns and infant weight gain and is recommended as part of the Dietary Guidelines for Americans. However, the use of responsive infant feeding can be challenging for many parents. Research is needed to assist caregivers recognize infant hunger or satiety cues and overcoming barriers to using responsive infant feeding. OBJECTIVE: The Learning Early Infant Feeding Cues (LEIFc) intervention was designed to fill this gap by using a validated coaching approach, SS-OO-PP-RR ("super," Setting the Stage, Observation and Opportunities, Problem Solving and Planning, Reflection and Review), to promote responsive infant feeding. Guided by the Obesity-Related Behavioral Intervention Trials model, this study aims to test the feasibility and fidelity of the LEIFc intervention in a group of mother-infant dyads. METHODS: This pre-post quasi-experimental study with no control group will recruit mothers (N=30) in their third trimester (28 weeks and beyond) of pregnancy from community settings. Study visit 1 will occur prenatally in which written and video material on infant feeding and infant hunger and satiety cues is provided. Demographic information and plans for infant feeding are also collected prenatally via self-report surveys. The use of responsive infant feeding via subjective (survey) and objective (video) measures is recorded before (study visit 2, 1 month post partum) and after (study visit 5, 4 months post partum) intervention. Coaching on responsive infant feeding during a feeding session is provided by a trained interventionist using the SS-OO-PP-RR approach at study visits 3 (2 months post partum) and 4 (3 months post partum). Infant feeding practices are recorded via survey, and infant weight and length are measured at each postpartum study visit. Qualitative data on the LEIFc intervention are provided by the interventionist and mother. Infant feeding videos will be coded and tabulated for instances of infant cues and maternal responses. Subjective measures of responsive infant feeding will also be tabulated. The use of responsive infant feeding pre-post intervention will be analyzed using matched t tests. Qualitative data will be examined to guide intervention refinement. RESULTS: This study initially began in spring 2020 but was halted because of the COVID-10 pandemic. With new funding, recruitment, enrollment, and data collection began in April 2022 and will continue until April 2023. CONCLUSIONS: After refinement, the LEIFc intervention will be tested in a pilot randomized controlled trial. The long-term goal is to implement LEIFc in the curricula of federally funded maternal-child home visiting programs that serve vulnerable populations-those that often have infant feeding practices that do not align with recommendations and are less likely to use responsive infant feeding. INTERNATIONAL REGISTERED REPORT IDENTIFIER (IRRID): DERR1-10.2196/44329.

Consequences of Ignoring Guessing Effects on Measurement Invariance Analysis.

Pseudo-guessing parameters are present in item response theory applications for many educational assessments. When sample size is not sufficiently large, the guessing parameters may be ignored from the analysis. This study examines the impact of ignoring pseudo-guessing parameters on measurement invariance analysis, specifically, on item difficulty, item discrimination, and mean and variance of ability distribution. Results show that when non-zero guessing parameters are ignored from the measurement invariance analysis, item discrimination estimates tend to decrease particularly for more difficult items, and item difficulty estimates decrease unless the items are highly discriminating and difficult. As the guessing parameter increases, the size of the decrease in item discrimination and difficulty tends to increase, and the estimated mean and variance of ability distribution tend to be inaccurate. When two groups have heterogeneous ability distributions, ignoring the guessing parameter affects the reference group and the focal group differently. Implications of result findings are discussed.

A Log-Linear Modeling Approach for Differential Item Functioning Detection in Polytomously Scored Items.

A log-linear model (LLM) is a well-known statistical method to examine the relationship among categorical variables. This study investigated the performance of LLM in detecting differential item functioning (DIF) for polytomously scored items via simulations where various sample sizes, ability mean differences (impact), and DIF types were manipulated. Also, the performance of LLM was compared with that of other observed score-based DIF methods, namely ordinal logistic regression, logistic discriminant function analysis, Mantel, and generalized Mantel-Haenszel, regarding their Type I error (rejection rates) and power (DIF detection rates). For the observed score matching stratification in LLM, 5 and 10 strata were used. Overall, generalized Mantel-Haenszel and LLM with 10 strata showed better performance than other methods, whereas ordinal logistic regression and Mantel showed poor performance in detecting balanced DIF where the DIF direction is opposite in the two pairs of categories and partial DIF where DIF exists only in some of the categories.

Detection Rates of the M2 Test for Nonzero Lower Asymptotes Under Normal and Nonnormal Ability Distributions in the Applications of IRT.

When considering the two-parameter or the three-parameter logistic model for item responses from a multiple-choice test, one may want to assess the need for the lower asymptote parameters in the item response function and make sure the use of the three-parameter item response model. This study reports the degree of sensitivity of an overall model test M2 to detecting the presence of nonzero asymptotes in the item response function under normal and nonnormal ability distribution conditions.

Estimation of an IRT Model by Mplus for Dichotomously Scored Responses Under Different Estimation Methods.

The purpose of this article is twofold. The first is to provide evaluative information on the recovery of model parameters and their standard errors for the two-parameter item response theory (IRT) model using different estimation methods by Mplus. The second is to provide easily accessible information for practitioners, instructors, and students about the relationships between IRT and item factor analysis (FA) parameterizations. Specifically, this is done using the "Theta" and "Delta" parameterizations in Mplus for unidimensional and multidimensional modeling with dichotomous and polytomous responses with and without the scaling constant D. The first objective aims at investigating differences that may occur when using different estimation methods in Mplus for binary response modeling. The second objective was motivated by practical interest observed among graduate students and applied researchers. The relations between IRT and Mplus FA "Theta" and "Delta" parameterizations are described using expressions without the use of matrices, which can be understood efficiently by applied researchers and students.

Validation and Reliability of the Korean Version of the Sport Anxiety Scale-2.

The main purpose of the present study was to examine the validation and reliability of the Korean version of the Sport Anxiety Scale (SAS-2Kr) by evaluating its factorial invariance across gender. A total of 303 Korean collegiate athletes (198 males and 105 females) from 9 sports participated in the study, and they completed the demographic questionnaire and the SAS-2Kr containing 15 items to measure multidimensional trait anxiety and individual differences in the cognitive and somatic anxiety experienced by athletes. The results of this study indicated that the construct validity in the SAS-2Kr was well established in that the values of the standardized factor loadings, composite reliability, and average variance extracted values were above the recommended cutoff points. The multiple-sample confirmatory factor analyses showed the SAS-2Kr could be generalizable across gender in college samples. The results also indicated that the SAS-2Kr supported the original 3-factor model of SAS-2 in English consisting of somatic anxiety, worry, and concentration disruption, and thus this study provides useful information for researchers to understand the athletes' tendency to experience anxiety reactions in sport situations. Suggestions for future research on competitive trait anxiety are provided in the discussion section.

Investigating the Behaviors of M2 and RMSEA2 in Fitting a Unidimensional Model to Multidimensional Data.

It has been widely known that the Type I error rates of goodness-of-fit tests using full information test statistics, such as Pearson's test statistic χ2 and the likelihood ratio test statistic G2, are problematic when data are sparse. Under such conditions, the limited information goodness-of-fit test statistic M2 is recommended in model fit assessment for models with binary response data. A simulation study was conducted to investigate the power and Type I error rate of M2 in fitting unidimensional models to many different types of multidimensional data. As an additional interest, the behavior of RMSEA2 was also examined, which is the root mean square error approximation (RMSEA) based on M2. Findings from the current study showed that M2 and RMSEA2 are sensitive in detecting the misfits due to varying slope parameters, the bifactor structure, and the partially (or completely) simple structure for multidimensional data, but not the misfits due to the within-item multidimensional structures.

Specifying Ability Growth Models Using a Multidimensional Item Response Model for Repeated Measures Categorical Ordinal Item Response Data.

When categorical ordinal item response data are collected over multiple timepoints from a repeated measures design, an item response theory (IRT) modeling approach whose unit of analysis is an item response is suitable. This study proposes a few longitudinal IRT models and illustrates how a popular compensatory multidimensional IRT model can be utilized to formulate such longitudinal IRT models, which permits an investigation of ability growth at both individual and population levels. The equivalence of an existing multidimensional IRT model and those longitudinal IRT models is also elaborated so that one can make use of an existing multidimensional IRT model to implement the longitudinal IRT models.

Exploring the Utility of Logistic Mixed Modeling Approaches to Simultaneously Investigate Item and Testlet DIF on Testlet-based Data.

This study explored the utility of logistic mixed models for the analysis of differential item functioning when item response data were testlet-based. Decomposition of differential item functioning (DIF) into item level and testlet level for the testlet-based data was introduced to separate possible sources of DIF: (1) an item, (2) a testlet, and (3) both the item and the testlet. Simulation study was conducted to investigate the performance of several logistic mixed models as well as the Mantel-Haenszel method under the conditions, in which the item-related DIF and testlet-related DIF were present simultaneously. The results revealed that a new DIF model based on a logistic mixed model with random item effects and item covariates could capture the item-related DIF and testlet-related DIF well under certain conditions.

Evaluating the Impact of Guessing and Its Interactions With Other Test Characteristics on Confidence Interval Procedures for Coefficient Alpha.

The effect of guessing on the point estimate of coefficient alpha has been studied in the literature, but the impact of guessing and its interactions with other test characteristics on the interval estimators for coefficient alpha has not been fully investigated. This study examined the impact of guessing and its interactions with other test characteristics on four confidence interval (CI) procedures for coefficient alpha in terms of coverage rate (CR), length, and the degree of asymmetry of CI estimates. In addition, interval estimates of coefficient alpha when data follow the essentially tau-equivalent condition were investigated as a supplement to the case of dichotomous data with examinee guessing. For dichotomous data with guessing, the results did not reveal salient negative effects of guessing and its interactions with other test characteristics (sample size, test length, coefficient alpha levels) on CR and the degree of asymmetry, but the effect of guessing was salient as a main effect and an interaction effect with sample size on the length of the CI estimates, making longer CI estimates as guessing increases, especially when combined with a small sample size. Other important effects (e.g., CI procedures on CR) are also discussed.

A Note on Parameter Estimate Comparability: Across Latent Classes in Mixture IRT Modeling.

The use of mixture item response theory modeling is exemplified typically by comparing item profiles across different latent groups. The comparisons of item profiles presuppose that all model parameter estimates across latent classes are on a common scale. This note discusses the conditions and the model constraint issues to establish a common scale across latent classes.

An Investigation of the Impact of Guessing on Coefficient α and Reliability.

Guessing is known to influence the test reliability of multiple-choice tests. Although there are many studies that have examined the impact of guessing, they used rather restrictive assumptions (e.g., parallel test assumptions, homogeneous inter-item correlations, homogeneous item difficulty, and homogeneous guessing levels across items) to evaluate the relation between guessing and test reliability. Based on the item response theory (IRT) framework, this study investigated the extent of the impact of guessing on reliability under more realistic conditions where item difficulty, item discrimination, and guessing levels actually vary across items with three different test lengths (TL). By accommodating multiple item characteristics simultaneously, this study also focused on examining interaction effects between guessing and other variables entered in the simulation to be more realistic. The simulation of the more realistic conditions and calculations of reliability and classical test theory (CTT) item statistics were facilitated by expressing CTT item statistics, coefficient α, and reliability in terms of IRT model parameters. In addition to the general negative impact of guessing on reliability, results showed interaction effects between TL and guessing and between guessing and test difficulty.

A Note on Statistical Hypothesis Testing Based on Log Transformation of the Mantel-Haenszel Common Odds Ratio for Differential Item Functioning Classification.

When differential item functioning (DIF) is investigated, DIF classification is made using statistical test results and estimated DIF sizes in practice. One of the well-known DIF classifications is that of the Educational Testing Service (ETS) A (negligible DIF), B (medium DIF), and C (large DIF) rules. This article provides a clarifying note on (a) a sketch of the proof of the asymptotic normality of what is known as the Mantel-Haenszel (MH) delta, which provides the basis of a point and an interval null hypothesis test based on the MH delta, and (b) how to conduct an interval null hypothesis test using the MH delta, which is necessary for the C DIF classification.

An investigation of DIF mechanisms in the context of differential testlet effects.

This study investigated differential item functioning (DIF) mechanisms in the context of differential testlet effects across subgroups. Specifically, we investigated DIF manifestations when the stochastic ordering assumption on the nuisance dimension in a testlet does not hold. DIF hypotheses were formulated analytically using a parametric marginal item response function approach and compared with empirical DIF results from a unidimensional item response theory approach. The comparisons were made in terms of type of DIF (uniform or non-uniform) and direction (whether the focal or reference group was advantaged). In general, the DIF hypotheses were supported by the empirical results, showing the usefulness of the parametric approach in explaining DIF mechanisms. Both analytical predictions of DIF and the empirical results provide insights into conditions where a particular type of DIF becomes dominant in a specific DIF direction, which is useful for the study of DIF causes.

Estimating a DIF decomposition model using a random-weights linear logistic test model approach.

A differential item functioning (DIF) decomposition model separates a testlet item DIF into two sources: item-specific differential functioning and testlet-specific differential functioning. This article provides an alternative model-building framework and estimation approach for a DIF decomposition model that was proposed by Beretvas and Walker (2012). Although their model is formulated under multilevel modeling with the restricted pseudolikelihood estimation method, our approach illustrates DIF decomposition modeling that is directly built upon the random-weights linear logistic test model framework with the marginal maximum likelihood estimation method. In addition to demonstrating our approach's performance, we provide detailed information on how to implement this new DIF decomposition model using an item response theory software program; using DIF decomposition may be challenging for practitioners, yet practical information on how to implement it has previously been unavailable in the measurement literature.

A multidimensional diagnostic perspective on academic achievement goal orientation structure, using the Rasch measurement models.

This study is designed to investigate a multidimensional structure of academic achievement goal orientations from a diagnostic perspective, using the Rasch measurement models. A data set of Korean students who responded to the Patterns of Adaptive Learning Survey (PALS) was analyzed. Both consecutive unidimensional and multidimensional Rasch measurement models were applied for comparative purposes. Each goal orientation dimension (i.e., the attitude) was standardized and then classified into three categorical levels, i.e., low, middle and high. These categorizations of goal dimensions were used to examine the role of students' performance-approach goals on mathematics achievement in relation with the other achievement goals. Results indicate that the multidimensional partial credit model was the best model with respect to the fit of the data to the models. Findings of the current study also demonstrate that practitioners who need specific feedback for instruction and/or intervention can benefit from the multidimensional approach.

Rasch modeling of accuracy and confidence measures from cognitive tests.

The use of IRT models has not been rigorously applied in studies of the relationship between test-takers' confidence and accuracy. This study applied the Rasch measurement models to investigate the relationship between test-takers' confidence and accuracy on English proficiency tests, proposing potentially useful measures of under or overconfidence. The Rasch approach provided the scaffolding to formulate indices that can assess the discrepancy between confidence and accuracy at the item or total test level, as well as at particular ability levels locally. In addition, a "disattenuated" measure of association between accuracy and confidence, which takes measurement error into account, was obtained through a multidimensional Rasch modeling of the two constructs where the latent variance-covariance structure is directly estimated from the data. The results indicate that the participants tend to show overconfidence bias in their own cognitive abilities.

Development of an emergency locking unit for a belt-in-seat (BIS) system using a MEMS acceleration sensor.

This paper proposes an emergency locking unit (ELU) for a seat belt retractor which is mounted on the back frame of a vehicle seat. The proposed unit uses a recliner sensor based on a MEMS acceleration sensor and solenoid mechanism. The seat has an upper frame supported to tilt on a lower frame. The retractor in belt in seat (BIS) system is supported by the upper frame. The proposed recliner sensor based on a MEMS acceleration sensor comprises orientation means for maintaining a predetermined orientation of emergency relative to the lower frame independently of the force of gravity when the upper frame tilts on the lower frame. Experimental results show that the developed recliner sensor unit operates effectively with respect to rollover angles. Thus, the developed unit will have a considerable potential to offer a new design concept in BIS system.

Random parameter structure and the testlet model: extension of the Rasch testlet model.

The current Rasch testlet model (RT) assumes independence of the testlet effect and the target dimension. This article investigated the impact of the violation of that assumption on RT and the performance of an extended Rasch testlet model (ET) in which the random parameter variance-covariance matrix is estimated without any constraints. Our simulation results showed that ET was the same or superior to RT in its performance. The target dimension variance in RT was the most strongly affected parameter and the bias of the target dimension variance was largest when the testlet effect was large and the correlation between the testlet effect and the target dimension was high. This suggests that in some real data applications, it may be difficult to accurately assess the size of testlet effect relative to the target dimension. RT showed close performance to ET with regard to item and testlet effect parameter estimation.